Deweese, Keith

Getzandanner, Kenneth

Liounis, Andrew

Shoemaker, Michael

Van Eepoel, John

Wright, Cinnamon

NASA Technical Reports Server

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National Aeronautics and Space Administration
Relative Terrain Imaging Navigation for the 
Asteroid Redirect Robotic Mission (ARRM)
Cinnamon Wright, John Van Eepoel, Andrew Liounis
Michael Shoemaker, Keith DeWeese, Kenny Getzandanner
https://ntrs.nasa.gov/search.jsp?R=20160001713 2019-08-31T04:22:11+00:00Z
Asteroid Redirect Mission (ARM) Concept
2
5 3
2
Outbound Cruise
Proximity Operations
Inbound Cruise
Earth
Moon
Earth Capture
Disposal
1 Launch &
Phasing
Similar to Option-A
Different from Option-A
Dispose of ARV and boulder
Longer duration at NEA target,
Allows for increased
Characterization and 
opportunities for secondary 
payloads
Near Earth Asteroid
Mars
Greater return ΔV for similar
Propellant quantity
Cruise to and approach asteroid
Crew Operations
Crew activities at boulder
6 LDRO Insertion
Insert into Lunar DRO
7
8
4
2
Not to scale
Operations conducted
Farther from the Sun and 
Earth; similar environment to a 
Mars-class mission
• Planned launch in December 2020 : Arrival at EV5 in October 
2022 : Return to Earth (with boulder) in late 2025
• Light times necessitate autonomous landing, boulder retrieval 
and ascent
ARRM Proximity Operations
• Key Events in Proximity Operations
– Transition from the 5 km hold point to 200 m waypoint on pre-defined burn
– 200 m waypoint to 50 m also performed on a pre-defined burn
– 50 m to 20 m descent and asteroid spin rate matching performed with closed 
loop control
– No thrusting towards surface after 20 m 3
ARRM Proximity Operations GNC Architecture
4
Retina Algorithms: Maplet Preprocessing
• Landmark
– Body-fixed surface location
• Maplet
– Local coordinate system 
and n x n grid centered on 
a landmark
– Contains height and albedo 
data
– Also called a digital 
elevation map (DEM)
• Tesselation
– Process of converting 
maplet into triangles in an 
efficient manner for 
intersection testing
– Surface normal data also 
computed
– Albedo data also preserved
5
VLM
UX
UY
UZ
UX
UY
Retina Algorithms: Predicted Image Generation
• Camera Model used to project maplet data onto image plane
– First done to determine range of pixels to render
– Second to project rays from camera focal plane to the maplet surface
• Rays that intersect surface geometry are then tested for a path to the 
Sun
• Use of several acceleration techniques used in ray tracing make the 
implementation tractable for an embedded system
6
Retina Algorithms:  Illumination Model
• The illumination model above is from McEwen 1991
• Beta is a weighting term to mix the Lambertian and 
Lommel-Seeliger components of the model
– The weighting factor, is chosen from experience.
• The images at right show good agreement between a 
synthetic image and one rendered with Retina
7
Synthetic Image
Predicted Image
• Definitions
– - surface normal
– - vector to the Sun
– - angle to the Sun
– - vector to vehicle
– - reflectance angle
– - phase angle
Retina Algorithms: Cross Correlation
• Uses Pearson moment correlation
– Other correlation methods are being explored to ensure robust 
performance.
• Correlation matrix created by shifting predicted image
– Magnitudes of shift determined by filter covariance
8
• i is the row in the image, j is the column
• is the predicted image pixel at row i, col j
• is the pixel value in the real image
• is the mean of pixels in the predicted image
• is the mean of pixels in the real image
• is the variance of pixels in the predicted image
• is the variance of pixels in the real image
Retina Algorithms: Sub-Pixel Peak Finding
• Comparison of correlation peak finding in SPC and Retina
– This example had no offset applied so truth is Row = 0.0, Column = 0.0
• Retina peak finding is a 3x3 grid that is linearly interpolated to find the 
peak to sub-pixel accuracy
– Current SPC implementations fit a paraboloid to the correlation surface
• Results obtained in Monte Carlo analysis show lower errors with linear 
peak finding.
9
Retina Performance
• Performance between SPC and Retina obtained for the ARRM descent from 
50 m to 10 m
• Perturbations applied include
– Position, attitude, camera parameters (focal length, distortion, etc), landmark 
knowledge, landmark resolution, knowledge of Sun direction
• Retina more robust because
– Registered every case while SPC did not
– SPC shows a bias for this scenario – investigating cause
10
Future Work
• Further testing implementation on SpaceCube 2.0
– Testing with 1 MP 10-bit depth images to utilize existing FlatSat
– Will test with higher resolution imagery to compare performance to the 
expected performance presented here
• Refine acceleration needs for current implementation
• Exploring improved correlation algorithms
• Continue assessing performance of Retina on additional scenarios
11
Questions
12
Backup
13
Retina Algorithms:  Illumination Model
• The illumination model above is from McEwen
• Beta is a weighting term to mix the Lambertian and 
Lommel-Seeliger components of the model
– The weighting factor, is chosen from experience.
• The images at right show good agreement between a 
synthetic image and one rendered with Retina 14
Synthetic Image
Retina Image
• Definitions
– is the normal to the 
surface
– is the angle to the 
Sun
– is the emission 
angle
– is the phase angle
Maplet
Surface 
Normal
Incidence 
Angle
Emission 
Angle


Relative Terrain Imaging Navigation for the Asteroid Redirect Robotic Mission (ARRM)

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